Digits and numbers are wonderful toys. The number of problems with them surpasses the imagination. Still, great minds think alike.

In 2013 I posed a classical problem to make as many numbers as possible by combining four fours.

In March I posed the challenge to make all the numbers of 0 to 20 by combining 5 5’s.

**1) 6 6’s ^{***/*****}**

Today’s problem is a sequel: make all the numbers 0 till 20 using 6 6’s. You can use brackets, +,-,*,/, ^and sqrt. You msy use ! for just one of the numbers.

You can check your solutions here and here

When googling, I found the puzzle masters at occupymath have posed the same challenge.

**2) 7 7’s ^{***/*****}**

Of course the problem can be generalized to 7 7’s. Make all numbers 0-24 using seven sevens, brackets, +-*/, no faculty.

You can check your solutions here and here

**3) general ^{***/*****}**

The next problem is not, as you may have thought, to make all numbers 0-20 with 8 8’s. Rather the question is, can the numbers 0-20 with made with all digits? In base 11, in base 12?

For a start:

0 = (n-n)*(n+…+n)

1 = n/n + (n-n)*(n+…+n)

2 = n/n + n/n + (n-n)*(n+ … + n)

and so on.